polchebyshev

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations provided, so the description carries the full burden. It states the computation but does not disclose any behavioral traits such as error conditions for invalid n, performance implications, or side effects. The schema already describes n as non-negative integer, but description adds no additional behavioral context.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Single sentence, zero waste, front-loaded with the core action. Every word earns its place.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a simple mathematical computation with two parameters and no output schema, the description is largely complete. It could mention that the result is a polynomial expression in variable v, but this is implied by the tool name and schema default. Overall adequate for its complexity.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100% (both n and v have descriptions). The tool description adds no extra meaning beyond what the schema provides. Baseline 3 is appropriate as the description does not augment parameter understanding.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

Description clearly states it computes the nth Chebyshev polynomial of the first kind. This is a specific verb+resource that distinguishes it from sibling polynomial tools like polcyclo, polhermite, and pollegendre.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

No guidance on when to use this tool versus alternatives. With many sibling polynomial tools, the description should explain that polchebyshev is for Chebyshev polynomials specifically, but it does not provide any usage context or exclusions.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.